The logarithm operator is the inverse operation of exponential. The subscript number is the base of the logarithm and the expression is what is being operated on. The relationship with exponets can be expressed using the two equations below:
By restricting the logarithm operator to base illustrates the pattern that the operator captures.
The exponential operator is closely related to the logarithm and radical operators. For example, given the scenario of exponential population growth, the relationship between the three operators is expressed below. Note, in this hypothetical scenario the initial population is represented with the value of .
Given the growth rate and the time elapsed, the exponent operator returns the population.
Given the growth rate and the population the logarithm operator returns the time elapsed.
Given the time elapsed and the population the radical operator returns the growth rate.